Econometrics Seminar - "Regression adjustment in randomized controlled trials: debiased estimation, accurate inference, and covariates selection"

Abstract. Randomized experiments have been widely applied in empirical research. In modern applications, researchers often have access to a large number of covariates, and the methods of covariates adjustments are commonly employed. Although the theory of point estimation for causal effects with many covariates has been well-studied in recent literature, theoretical analyses on covariates selection and uncertainty quantification are still under-developed. In this paper, we propose Mallows type optimal covariates selection criteria to minimize the approximate mean squared error of a point estimator, and develop a higher-order accurate standard error under many covariates.

Abstract. This paper is concerned with estimation and inference on average treatment effects in randomized controlled trials when researchers observe potentially many covariates. By employing Neyman’s (1923) finite population perspective, we propose a bias-corrected regression adjustment estimator using cross-fitting, and show that the proposed estimator has favorable properties over existing alternatives. For inference, we derive the first and second order terms in
the stochastic component of the regression adjustment estimators, study higher order properties of the existing inference methods, and propose a bias-corrected version of the HC3 standard error. The proposed methods readily extend to stratified experiments with large strata. Simulation studies show our cross-fitted estimator, combined with the bias-corrected HC3, delivers precise point estimates and robust size controls over a wide range of DGP